Can a custom filter read property value and use it?
Yes you can have a game property in a GLSL shader.

Here is a good read on making exactly what you want, a blur filter with a controlled blur amount from a game property (plus blend file).

From the script linked above, you can just use the property name blur_amount in the GLSL script.

Declare the var like this, then use blur_amount however you want to.

uniform float blur_amount;